Express this quotient in scientific notation: ${\frac{8.700\times 10^{-1}} {10.0\times 10^{2}}}$
Answer: Start by collecting like terms together. $= {\frac{8.700} {10.0}} \times{\frac{10^{-1}} {10^{2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.87 \times 10^{-1\,-\,2}$ $= 0.87 \times 10^{-3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.87$ is the same as $8.70 \div 10$ , or $8.70 \times 10^{-1}$ $ = {8.70 \times 10^{-1}} \times 10^{-3} $ $= 8.70\times 10^{-4}$